Etude asymptotique des enlacements du mouvement Brownien autour des droites de l'espace
The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies by \textit{J. W. Pitman} and the second author [see, e.g. ''Asymptotic laws of planar Brownian motion.'' Ann. Probab. 14, 733-779 (1986)] and the authors [see e.g. Probab. Theory Relat. Fields 71, 183-229 (1986; Zbl 0579.60077)], of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points. The following principle governs the passage from results in the plane to results in space: Let B be a three dimensional Brownian motion, and \(P_ 1,...,P_ k\), k planes which intersect two by two. Then, the convergence in distribution concerning the planar Brownian motion \(B^ i\) (1\(\leq i\leq k)\), defined respectively as the orthogonal projections of B on \(P_ i\) (1\(\leq i\leq k)\) take place jointly, and the corresponding limit variables are independent.
asymptotic distribution for the windings of a three-dimensional Brownian motion
scientific article; zbMATH DE number 3956161
scientific article